Question

Describe the right-hand and the left-hand behavior of the graph of t(x)= 4x^5 - 7x^3 - 13. Does it rise or fall left or right

Answer 1

see explanation

Explanation:

To determine the end behaviour, we only need to consider the term of highest degree, that is the leading term in standard form

The term of highest degree in f(x) is 4
`x^(5)`

which is of odd degree with positive coefficient

As a result the end behaviour is

As x → + ∞ (right), f(x) → + ∞ ( that is rises )

As x → - ∞ (left), f(x) → - ∞ ( that is falls )